2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94439Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with $\dbar$-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite codimension in the space of independent variables. For higher $\dbar$-index these hierarchies represent themselves families of multidimensional equations with multidimensional constraints. The $\dbar$-dressing method is used to construct these hierarchies. Hidden KdV, Boussinesq and hidden Gelfand-Dikii hierarchies are considered too.45 pages, LaTeX 2.09 with epsf,amstex and amssymb stylesExactly Solvable and Integrable Systemstext